The Dust Environment of Comet 67P/Churyumov-Gerasimenko

A&A 422, 357–368 (2004) Astronomy DOI: 10.1051/0004-6361:20035806 & c ESO 2004 Astrophysics

The dust environment of comet 67P/Churyumov-Gerasimenko

M. Fulle1, C. Barbieri2,G.Cremonese3,H.Rauer4, M. Weiler4, G. Milani5, and R. Ligustri6

1 INAF - Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34131 Trieste, Italy 2 Dipartimento di Astronomia, Universit`a di Padova, Vicolo dell’Osservatorio 2, 35122 Padova, Italy 3 INAF - Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy 4 Institute of Planetary Research, DLR Rutherfordstrasse 2, 12849 Berlin, Germany 5 Unione Astroﬁli Italiani, UAI 6 Osservatorio di Talmassons, CAST, Talmassons (Ud), Italy

Received 4 December 2003 / Accepted 6 April 2004

Abstract. The new target of the ESA Rosetta Mission is comet 67P/Churyumov-Gerasimenko, which passed its last perihelion on 18 August 2002 and was well observed from fall 2002 to spring 2003. Its most prominent feature was a thin dust tail, which is best ﬁtted by the Neck-Line model. Fits of the whole tail provide the dust environment of 67P during a year around perihelion; it shows a strong asymmetry between pre and post perihelion times. The dust mass loss rate appears constant since 2 AU before perihelion at about 200 kg s−1, a factor 100 higher than 46P/Wirtanen, the previous Rosetta target. Neck-Line photometry during 2002 and 2003 suggests that such a dust environment has remained similar since 3.6 AU before perihelion, i.e. the distance at which Rosetta science operations will start and the lander will be delivered to the surface.

Key words. space vehicles – comets: general – comets: individual: 67P/Churyumov-Gerasimenko

1. Introduction observability after the perihelion passage of August 18, 2002: before August 2002 and after spring 2003, the comet was too Due to a launch delay, in February 2003 ESA changed the tar- close to the Sun to be observable. We will analyse in another get of the Rosetta Mission (ESA 2003): from 46P/Wirtanen paper the data collected before the 1996 perihelion passage. to 67P/Churyumov-Gerasimenko (67P hereafter for brevity). During 2002 and 2003, 67P showed a 10 arcmin long and thin A strong effort was required to obtain information on the new tail (Fig. 1), bright enough to be monitored by CCD cameras of target in order to change the orbiting strategies to adapt the al- amateur astronomers. This is unusual for short-period comets, ready built spacecraft and instruments to an environment pos- which rarely show bright tails. We will show in this paper that, sibly different from the planned one: this regards not only the certainly during all spring 2003, and probably also during fall shape and size of the nucleus, but also the coma environment, 2002, this tail was a dust tail. If ground-based observations only which is related to shape and spin state of the nucleus. Here we are available, models of dust tails provide the most complete focus on the dust environment of 67P: a comparison with the information on a comet dust environment (Fulle 1999). Coma environment of the previous target 46P will allow us to outline photometry, quantified by the quantity Afρ (A’Hearn et al. the differences between two well studied short-period comets, 1984), will then be used to constrain the outputs of dust tail in order to understand if 67P is representative of the family of models. These suggest that the dust environment of 67P may short-period comets. Moreover, a model of the dust environ- be different from that of typical short-period comets, in which ment is necessary to plan the operations of the many instru- such a long lasting dust tail was never observed. Therefore, a ments studying the dust ejected from the comet, to determine deep analysis of the dust environment of 67P is even more im- the orbiting strategies, the software robustness of the naviga- portant in the perspective of the Rosetta Mission. tion cameras against false nucleus detection, and the lifetime Let us recall that one of the difficulties in interpreting dust of the landing probe against dust pollution. images is that the dust ejections occurring days before, months In this paper we consider IRAS observations performed before or years before the time of observation form patterns in 1983 (Sykes & Walker 1992) and ground-based data col- which may have a similar appearance. Therefore, extreme care lected on the dust ejected from 67P during the nine months of must be paid to obtain a correct identification. If an observed Send offprint requests to: M. Fulle, e-mail: [email protected] pattern is improperly identified, the derived time (and in gen- Based also on observations collected at the National Galileo eral the rate) of dust production will be severely in error. In Telescope and the 2 m telescope of the Thüringer Landessternwarte the case of 67P, the identification of the thin tail in terms of Tautenburg. a trail (Sykes & Walker 1992) or in terms of a Neck-Line

Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20035806 358 M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko

Table 1. The observed Position Angle PAT of the Tail is compared with the antisolar direction (Position Angle PARV of the prolonged radius vector) and the expected position of the dust trail (Position Angle PACO of the comet orbit projected on the sky). The observed PAT values are best ﬁt by the computed PANL of the Neck-Line ejected at Sun-Comet distances r(θ−π)andatthet(θ−π)−T times (days with respect to perihelion T), where θ is the comet true anomaly at observation. Observers: DT, Diego Tirelli; RL, Rolando Ligustri (Talmassons Observatory); HM, Hermann Mikuz (Crni Vrh Observatory); TNG, National Galileo Telescope; TLS, Tautenburg Schmidt Telescope at Th¨uringer LandesSternwarte.

Time UT t(θ) − Tr(θ) θ t(θ − π) − Tr(θ − π)PANL PA CO PA RV PA T Band Observer [days] [AU] [◦] [days] [AU] [◦][◦][◦][◦]

14.094 Aug. 2002 –4.219 1.29 –3.6 – – – 263.7 272.4 270 ± 3 R RL 8.107 Sep. 2002 21.794 1.32 18.4 –810 5.28 275.4 274.6 283.3 280 ± 3 V DT 19.134 Oct. 2002 62.821 1.49 48.4 –378 3.62 289.8 288.6 293.5 290 ± 3 V DT 8.059 Nov. 2002 82.746 1.61 60.7 –285 3.05 294.2 293.9 295.0 294 ± 3 R RL 11.154 Nov. 2002 85.841 1.63 62.4 –275 2.99 294.7 294.6 295.1 296 ± 3 V DT 4.175 Jan. 2003 140.862 2.03 86.3 –164.2 2.20 299.3 303.9 291.0 296 ± 3 V DT 11.188 Jan. 2003 147.875 2.08 88.7 –156.4 2.14 299.3 304.3 289.6 297 ± 3 R RL 12.197 Jan. 2003 148.884 2.09 89.0 –155.3 2.13 299.3 304.4 289.4 295 ± 3 R RL 2.003 Feb. 2003 167.690 2.23 94.8 –138.0 2.00 298.6 303.9 282.7 297 ± 3 R RL 22.935 Mar. 2003 216.622 2.58 107.0 –107.7 1.78 294.6 297.6 138.7 296 ± 2 R HM 27.000 Mar. 2003 220.687 2.61 107.8 –105.8 1.77 294.4 297.1 133.2 294.5 ± 0.5 R TNG 27.875 Mar. 2003 221.562 2.62 108.0 –105.4 1.76 294.3 297.0 132.2 294.0 ± 0.5 R TLS 28.028 Mar. 2003 221.715 2.62 108.1 –105.3 1.76 294.3 297.0 132.0 294.0 ± 0.5 R TLS 28.896 Mar. 2003 222.583 2.63 108.2 –104.9 1.76 294.3 296.9 131.1 294.0 ± 0.5 R TLS 6.922 Apr. 2003 230.609 2.69 110.1 –101.0 1.73 294.0 296.2 124.5 294 ± 2 R HM

2. 67P Tail: Evolution over nine months Databases of the Comet Section of the Italian Amateur Astronomer Union (UAI) contain many CCD images following the evolution of the thin tail during the whole 2002/03 observability window (UAI 2003). These images are filtered using broadband filters only, like Cousins R, and are here comple- mented by four images of much higher quality obtained at the National Galileo Telescope and the Tautenburg Schmidt Telescope (Weiler et al. 2004a, Fig. 1). The log of all the observations analysed in this paper is reported in Table 1. Here we report also the correspondence among UT times, the comet true anomaly θ (i.e. the angle between the Sun-Comet and the Sun-perihelion vectors), the observation time related to perihe- Fig. 1. Image of the thin tail of 67P taken on 27.875 March 2003 UT lion t(θ) − T, and the Sun-Comet distance r(θ): in the following at the 2 m Tautenburg Schmidt Telescope (see Table 1 for details of sections and figures, Table 1 can be used to convert one of these the observations). 67P showed a similar tail during nine months after 2002 perihelion. The axis units are pixels, with scale 1.23 arc- quantities to the others. sec pixel−1 (the scale reported in Weiler et al. (2004a) is wrong). The The 67P tail is so thin that it can be described as a image width is 9×105 km projected at the Earth-comet distance. North linear spike leaving the coma with a sky-projected Position ◦ ◦ is up. The antisolar and tail Position Angles are 132 and 294 ,re- Angle PAT. This can be compared to the Position Angle PARV spectively, both rotating anticlockwise from North (PARV and PAT in of the prolonged radius vector (i.e. the antisolar direction pro- Table 1). A factor two intensity step was chosen between isophotes. jected on the sky) and to the Position Angle PACO of the comet orbit projected on the sky. If the thin tail is a trail, we must have PAT = PA CO. The data in Table 1 allow us to exclude that the thin tail is the IRAS trail. If the tail is an ion tail, (Kimura & Liu 1977) might shift the same dust production PA T must be always close to PARV . More precisely, the 67P from 1.3 AU up to 3.6 AU pre-perihelion: the difference is of orbital velocity is less than 35 km s−1; the solar wind radial extreme significance for the Rosetta Mission. We will show that velocity is greater than 400 km s−1, while its tangential com- the thin tail analysed here cannot be identified with the IRAS ponent is less than 50 km s−1 (Brandt et al. 1972); it follows ◦ trail, which is orders of magnitude fainter and does not fit the that |PA T − PA RV | < 10 . The data in Table 1 show that the tail tail position on the sky. We will compare the estimates of the could have been an ion tail during 2002, but this was impossi- dust loss rates provided by models of dust tails and IRAS trails. ble during 2003. If PARV < PA T < PA CO while PARV < PA CO M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko 359

is one of the two parameters (the other is the starting velocity of the dust) determining the orbit of the grain, Cpr = 1.19 × 10−3 kg m−3 depends on the light velocity, Solar mass and gravitation constant, Qpr depends on the chemical composition of the grains and is close to one for the presumably large absorbing grains in the 67P tail (Burns et al. 1979; the fact that the 67P tail is composed by mm-sized grains is confirmed by all models), ρd is the dust bulk density and d is the dust diameter if grains are spheres, or the mean size if grains are aspherical but compact (i.e. far from fractal or strongly elongated shapes). If we consider dust grains ejected in all directions at the same time with the same β and with the same velocity, we obtain a spherical shell expanding in space. In a cometocentric Fig. 2. Peak surface brightness of the thin tail observed during 2002 reference frame, this shell is expected at first sight to maintain and 2003. Before perihelion, the much fainter tail is probably an ion its spherical shape for all future times, but this naive conclu- tail. For t − T > 50 days the tail brightness remains fairly constant, sion is wrong, because it does not take into account that the suggesting that the dust tail is characterized by a constant dust cross cometocentric reference frame is not inertial. If, in the inertial section. The magnitudes were corrected for the changing Sun-Comet heliocentric reference frame, we take into account the helio- − distance r. See Table 1 for the relationship among t T,UTandr. centric keplerian orbit of each grain composing the spherical shell, we can compare dust orbits to the comet orbit: these two and PACO < PA T < PA RV while PACO < PA RV , then the orbital planes intersect one another along a nodal line crossing tail can be a dust tail. The data in Table 1 show that this in- the Sun, with the first node at the dust ejection and the sec- terpretation is consistent with all available observations. After ond node again crossing the orbit plane of the comet nucleus at ◦ February 2003, the PAT and PARV data show that the thin tail a true anomaly exactly 180 after the ejection. The shell cen- was apparently pointing towards the Sun. However, the con- ter motion is that of a particle with the same β ejected at zero dition PARV < PA T < PA CO was always satisfied, so that in velocity, so that its positions are given by classical syndyne- 3D space the thin tail was always placed outside the comet or- synchrone computations: it moves in the comet orbital plane. bit. In other words, after February 2003 the tail was simply a Monte Carlo simulations (Fulle & Sedmak 1988) have shown perspective antitail, but we will continue to call it thin tail. that, when the shell center reaches a true anomaly exactly 180◦ Since October 2002, all CCD images show a tail with after the ejection, the shell can be well approximated by an el- almost perfectly constant shape and brightness (Table 1). lipsoid (Fig. 3), whose two main axes in the comet orbital plane − Figure 2 shows the peak mag arcsec 2 of the thin tail between are approximately given by the ejection velocity times the flight August 2002 and April 2003, after we have subtracted 5 log r time, and are orders of magnitude longer than the axis perpen- to correct for the changing Sun-Comet distance r (the surface dicular to the comet orbital plane: we can approximate such brightness does not depend upon the changing Earth-Comet an ellipsoid with a 2D ellipse shrunk on the same plane. If the distance). For t −T > 50 days, the tail brightness remains fairly observer is close to this plane, all the dust is confined in an in- constant, suggesting that the total dust cross section remained finitesimally thin sky area, forcing the shell brightness to rise constant (within a factor 3) since October 2002. Around peri- to very high values. helion the tail is much fainter: it could be either an ion tail or If we consider shells of many β values, we obtain a long a dust tail composed of small grains ejected at perihelion only, spike starting from the comet nucleus which is much brighter much fainter than the dust tail appearing after perihelion. than the surrounding tail and is named Neck-Line. In case of anisotropies of dust ejection and velocity, due both to nu- 3. Neck-Line models cleus inhomogeneity and asphericity and to the dust-gas in- teraction in the coma, the shells acquire a 3D shape more Kimura & Liu (1977) were the first to point out that on long complex than ellipsoids, but always these 3D shells are well time scales the heliocentric motion of the dust particles build- approximated by 2D figures (more complex than ellipses) at ing up cometary dust tails has strong consequences on all the second orbital node. In fact, Monte Carlo simulations observable structures belonging to dust tails: Neck-Lines are have confirmed that the singularity generated by the dust among the most prominent ones when the Earth is close to the shell collapse implies a brightness maximum well observable comet orbital plane, and this condition was always satisfied for any ejection anisotropy, and continuous temporal evolu- ◦ during 2002 and 2003 thanks to the very low inclination (7 ) tion of the dust loss rate and size distribution (Cremonese of the orbital plane of 67P with respect to the ecliptic. To un- & Fulle 1989). Fulle (1988) has also provided an analytical derstand Neck-Lines it is necessary to introduce the concept of proof that the Neck-Line brightness must rise to infinity when dust shells ejected by the inner coma of the comet. Let us con- the observer crosses the comet orbital plane. In such a limit- sider dust of a single β ejected at a single time from the comet ing case the opacity of the dust grains comes into play and nucleus. Here: limits the brightness to a finite value. Neck-Lines were ob- C Q served in many comets: Arend-Roland (Kimura & Liu 1977), = pr pr β (1) Bennett (Pansecchi et al. 1987; Fulle & Sedmak 1988), Halley ρdd 360 M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko

Fig. 3. Comparison among three different dust shells composed of dust of fixed β and ejected at fixed times with fixed ejection velocities. The shells are followed in their heliocentric orbits and then projected on the sky at the TNG observation (see Table 1 for the observation log; at this time the thin tail appeared as a perspective antitail; a factor two intensity step was chosen between isophotes). The prolonged radius vector is the vector r (Table 1) crossing the comet nucleus and prolonged outside the comet orbit, so that in all the panels the Sun is at image bottom. The comet nucleus position is exactly at x = y = 0 (the brightness peak to the upper left of the nucleus is a star). Left panel: shell composed of grains of β = 1.5× 10−4 ejected at 3 m s−1 at 105.8 days before 2002 perihelion. Central panel: shell composed of grains of β = 5× 10−6 ejected at 0.12 m s−1 at the 1996 perihelion. Right panel: shell composed of grains of β = 2.5 × 10−6 ejected at 0.06 m s−1 at the 1989 perihelion. The sample clustering is due to the 10−6 ratio between dust and comet nucleus orbital velocity.

(Cremonese & Fulle 1989), Austin (Fulle et al. 1993) and oth- that since October 2002 the observed tail was a Neck-Line, ers (e.g., Hale-Bopp at the beginning of 1998). It is probable composed of dust ejected at times t(θ−π) and at Sun-Comet dis- that all the perspective months-old antitails observed in the tances r(θ − π), diﬀerent for each observation. The Neck-Line past (e.g., Sekanina & Schuster 1978) were in fact Neck-Lines. maintained an almost constant brightness since October 2002 Neck-Lines ejected after perihelion could be observed before (Fig. 2): this implies that the total cross section of the ejected the following perihelion of periodic comets. However, the time dust was constant (within a factor 3) from 3.6 AU to 1.7 AU between ejection and observation is so long (close to the comet before perihelion (see the r(θ − π) values in Table 1). orbital period) that the dust shells become long strings (Fig. 3), whose sky surface density is independent of the observation 4. Dust from previous perihelion passages geometry.

In Table 1 we report the computed Position Angle PANL At observation wavelengths of 12 µm, 25 µm and 60 µm, the of the 67P Neck-Line, which changes by only 5◦ during the IRAS satellite (Sykes & Walker 1992) detected a trail of 67P, ◦ ◦ whole of 2003, while the antisolar direction PARV changes by 1.1 long behind the coma, and 0.1 ahead the coma. The trail about 180◦. Therefore, the apparent direction of the Neck-Line length allowed Sykes & Walker (1992) to conclude that the changes from an anti-sunward to a sunward spike. After whole 67P trail was ejected during the previous perihelion pas- October 2002, all the computed PANL values fit the ob- sage. Reach et al. (2003) suggested that dust released at the served PAT values within the measurement errors. Moreover, previous perihelion (January 1996) could have built up the thin a Neck-Line is expected after February 2003, appearing as tail of Fig. 1, which in this case should be identified with the a very thin perspective spike-like antitail. We can conclude IRAS trail (in fact, a trail can be defined as the dust tail ejected M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko 361 during previous perihelion passages). Then, the presumably the nucleus surface will fall back on the nucleus, while a neg- large activity at the 1996 perihelion could explain the appear- ligible fraction only will leave the coma with v vesc (Crifo ance of a bright dust trail during 2002 and 2003. To check this et al. 2004). To obtain an observable fraction of such boulders, hypothesis, we use again the concept of dust shells: we con- their loss rate at the 1996 or 1989 perihelia should have been so sider a fixed time of dust ejection, a fixed β, and consider dust large as to be inconsistent with the observed coma brightness. ejected in all the possible directions with a fixed velocity. Models based on extremely anisotropic ejections at previous Here we compare the Neck-Line and the trail interpreta- perihelion passages cannot solve the problem either. To obtain tions, by projecting on the sky dust shells exactly at the time of the shells plotted in Fig. 3 with much larger β values, all the the TNG observation (Table 1): the comparison between the dust must have been ejected in sectors covering infinitesimal TNG CCD image (Fig. 3) and the sky-projected shells will fractions of the solid angle: realistic physical dust-gas interac- allow us to check the reliability of the hypothesis. The shell tion can neither reproduce such a finely collimated lonesome ejection times are fixed: 1989 perihelion, 1996 perihelion and dust jet, nor change the direction of such a jet to fit the tail 105.8 days before the August 2002 perihelion (this last time is orientation at all observation times. provided by t(θ − π) − T in Table 1 for the TNG observation). We must conclude that the thin tail shown in Fig. 3 is not The β and ejection velocity values are constrained by this fact: a trail. This means that the 67P IRAS trail must be fainter than the TNG image shows that the brightness of the thin tail de- the observed thin tail. The IRAS trail was wider (5 × 104 km) creases by a factor 10 at least from the coma up to 3 × 105 km than the thin tail shown in Fig. 3. Sykes & Walker (1992) derive sunward (Fig. 3): therefore, the dust shell cannot be larger than an optical depth τ = 2 × 10−9 of dust at the brightness peak the size of Fig. 3, otherwise we cannot fit such a fast brightness of the trail, so that we can compute the corresponding peak drop. optical brightness if we assume that the dust area emitting at To compute the dust motion lasting up to 15 years, we ne- IR wavelengths is the same area that is scattering the sun light: glect planetary perturbations. In fact, we consider very large this is correct because the dust sizes in the trail are certainly grains, orbiting very close to the comet nucleus: it is probable much larger than both optical and IR wavelengths. Then that planetary perturbations in the course of the 15 years affect π (δr)2 the grains in exactly the same way they affect the comet nu- m = m + 2.5log (3) trail A τ cleus. Moreover, the orbital parameters of 67P have remained p −2 almost constant since 1989: the three angles describing the where mtrail is the trail peak mag arcsec in the same pass- ◦ comet orbit orientation changed by less than 0.1 , while the band as the Solar magnitude m, δ = 206 265 arcsec, r is the perihelion distance and eccentricity changed by less than 1% Sun-Comet distance in AU, Ap is the albedo, set here to 4%. We (Yeomans & Wimberly 1991). Since we are considering grains obtain that the IRAS trail is fainter than 28.0 mag arcsec−2 in orbiting very close to the nucleus, the differences between the the R passband. This proves that the IRAS trail is much fainter orbital angles of grains and of nucleus will be much lower than the thin tail observed during 2002 and 2003 (Fig. 2), con- ◦ than 0.1 and the difference between perihelion distance and firming the conclusions already reached considering the dis- eccentricity of each grain and of the nucleus will be lower agreement between PAT and PACO in Table 1. On the other than 1%. hand, since the Neck-Line is much brighter than the trail, The left panel of Fig. 3 shows the sky-projected dust shell IRAS must have observed it. However, the poor angular reso- − composed of grains with β = 1.5 × 10 4 (corresponding to a lution (the IRAS cameras had pixels 2 arcmin wide, equivalent 3 −3 −1 diameter of 0.8 cm if ρd = 10 kg m ) ejected at 3 m s at to 100 pixels in Fig. 1) prevented IRAS from disentangling the 105.8 days before 2002 perihelion. This is a Neck-Line shell two dust structures in the sky: the Neck-Line remained con- perfectly fitting the Position Angle of the observed thin tail. fused in the first 5 pixels of the trail observed by IRAS. The central panel of Fig. 3 shows the sky-projected dust shell composed of grains of β = 5 × 10−6 (corresponding to a diam- 3 −3 −1 5. Neck-Line photometry eter of 24 cm if ρd = 10 kg m ) ejected at 0.12 m s exactly at the 1996 67P perihelion. The right panel of Fig. 3 shows the The images showing the longest Neck-Line of 67P were taken sky-projected dust shell composed of grains of β = 2.5 × 10−6 at the Tautenburg Schmidt Telescope during the nights of 27 3 −3 (corresponding to a diameter of 48 cm if ρd = 10 kg m ) and 28 March, 2003 (Fig. 1, Weiler et al. 2004a). The CCD field ejected at 0.06 m s−1 at the 1989 67P perihelion. These last two of this telescope is much wider than that of the TNG Telescope. shells do not fit the Position Angle of the observed thin tail: the Therefore, the Neck-Line data from these images allow us to difference is larger than 3◦, much larger than the small uncer- explore the dust population at the smallest sizes we are able tainties introduced by planetary perturbations occurring during to detect (the farther the dust from the nucleus, the smaller the 15 years. The preceding dust velocities are much lower than the grains in the Neck-Line). We take into account only R-filtered expected escape velocity vesc from the 67P nucleus. Assuming images to increase the S/N ratio. In Table 2 we describe the a nucleus radius Rn = 2 km (Lamy et al. 2003), we get geometry of the Tautenburg observations and the angles defin- ing the expected orientation of the Neck-Line: the observed ρ R v = 0.75 n n ms−1 > 0.5ms−1 (2) Position Angle of the Neck-Line PA coincides with the com- esc 103 kg m−3 1km T puted PANL within the measurement accuracy (Table 1). for reasonable nucleus densities ρn. Since the gas coma is prob- By means of simple analytical formulae, the Neck-Line ably inhomogeneous, most of the meter-sized boulders leaving model allows us to obtain both the β-dependence of the dust 362 M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko

Table 2. Geometry of Neck-Line Observations. Time: March 2003. r and ∆: Sun-Comet and Earth-Comet distances at observation. λ:Earth cometocentric latitude on the comet orbital plane. Φ: phase angle. PARV : Position Angle of the antisolar direction. s, a and b: geometric parameters of the Neck-Line (see Eq. (5)). αµ + ατ: predicted Angle between the antisolar direction and the Neck-Line axis. tejection: time of ejection of the dust composing the Neck-Line (days related to comet perihelion).

◦ ◦ ◦ 11 −8 −1 −6 −1 ◦ Time [UT] r [AU] ∆ [AU] λ [ ] Φ [ ]PARV [ ] s [10 m] a [10 s ] b [10 s ] αµ + ατ [ ] tejection [days] 27.875 2.621 1.694 2.9 10.1 132.19 9.50 1.447 0.978 162.14 –105.37 28.028 2.622 1.696 2.9 10.1 132.03 9.50 1.447 0.981 162.29 –105.30 28.896 2.628 1.707 2.8 10.4 131.14 9.50 1.449 0.993 163.15 –104.90 velocity (and its absolute values in m s−1 for each β value), and the β-distribution, which is related to the dust size distribution. If we assume a constant dust bulk density in the relatively small β interval actually covered by the Neck-Line (a factor 6 only between the largest and smallest β values), we immedi- ately obtain the u value (power index of the dust ejection ve- u locity versus the dust radius s, v = v0 (s/s0) ), and the power index α of the differential dust size distribution. In fact, Fulle & Sedmak (1988) have developed the photometric theory of the Neck-Lines and obtain that, if this condition is satisfied: v(β) <βsa (4) then the sky surface brightness of the Neck-Line is Fig. 4. Dust velocity function provided by the Neck-Line model ap- F(t,β) ax b2y2 plied to Tautenburg Schmidt CCD images. Diamonds: width of the D(x,y) = 1 + er f exp − (5) = b × s v(β) v(β) v2(β) Neck-Line (converted to dust velocity v width) at several x axis positions (converted to β = x/s, b and s in Table 2). Dotted where F is the β distribution, s, a and b are geometrical pa- line: threshold√ of validity of the analytical approximations (Eq. (4)). rameters of the Neck-Line (listed in Table 2 for the Tautenburg Dashed line: β curve, corresponding to u = −1/2inFigs.6and7. observations), v(β) is the dust ejection velocity, and x and y define an image reference frame oriented as follows: x lies exactly along the Neck-Line axis, while y is exactly perpendicular to the Neck-Line axis. Equation (5) shows that, when we measure the half-width of the Neck-Line along the y direction, we directly measure the dust velocities at given β values: only this method is able to provide such direct information from ground based observations. Then, the brightness measured along the Neck-Line allows us to compute the F values. If we fit F by means of a power law with index γ, we get the power index α = −γ − 4 of the corresponding differential dust size distribution at the nucleus. Figure 4 shows the results regarding the dust ejection velocity. From Table 2 we obtain that all the data from all the three Tautenburg observations provide information on the dust ejec- Fig. 5. β distributions obtained by the photometric theory of Neck-Lines applied to the same Tautenburg Schmidt images already tion that occurred during 10 hours only at t − T = −105 days. analysed in Fig. 4. Diamonds: β-distribution F obtained by means of We can consider constant the mean dust environment of the Eq. (5) (see text for discussion). Dotted line: β distribution with power comet during these 10 h, so that we can refer all data to a sin- index γ = −0.5, corresponding to α = −3.5. Dashed line: β distribu- gle dust velocity function. This is important because we can tion with power index γ = −1, corresponding to α = −3. extract few data from each image: many star tracks pollute the photometric data of the Neck-Line, and since these tracks dif- fer in orientation by less than 30◦ with respect to the x-axis to measure 14 width and brightness values of the Neck-Line. (Fig. 1), every directional filtering removing the stars would af- The widths are already converted into velocities in Fig. 4 by fect the width of the Neck-Line we need to measure. We prefer means of the b parameter (Table 2). The dashed line is the best to select in each image the Neck-Line sector which is not pol- β power law fitting the points, yielding u = −1/2. luted by any track. This reduces the number of useful sectors Figure 5 shows the results regarding the β distribution, i.e. in each data set. Collecting together all the results, we improve the brightness values along the x-axis converted into F by the sampling of the F and v functions. In total we were able means of Eq. (5). The F values can be fitted by any power M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko 363

Fig. 6. Image of the tail of comet 67P obtained on 27.0 March 2003 by means of the TNG Galileo Telescope at La Palma. In all the panels the Sun is at the bottom. A factor two intensity step was chosen between isophotes. Continuous lines: isophotes of the observed image. Dashed lines: isophotes of the model tail computed by means of the inverse tail model adopting the dust parameters summarized in Fig. 7. The panels refer to different combinations of the w and u parameters. w refers to the anisotropy of dust ejection: w = 180◦ for perfectly isotropic dust ejection from the inner coma; w = 90◦ for dust ejection confined to the half coma facing the Sun; w = 45◦ for dust ejection confined within a cone with its axis pointing to the Sun and with a half width of 45◦. u models the dependence of the dust ejection velocity v on the dust radius s: u v = v0(s/s0) (v0 and s0 are shown in Fig. 7). The value u = −1/2 obtained in Fig. 4 was adopted. index γ between –0.5 and –1, implying −3.5 ≤ α ≤−3.0. of the Galileo Telescope (TNG) at La Palma on the night be- This result refers to the β range shown in Figs. 4 and 5, cor- tween 26 and 27 March, 2003. We selected all the obtained responding to dust sizes from 1.5 mm to 1 cm if we consider R CCD images and added them to obtain an input image to 3 −3 valid Eq. (1) with ρd = 10 kg m . The fact that α ≥−3.5 be processed by means of the inverse tail model (Fulle 1989). would be further confirmed if we took into account the fact Isophotes of the tail image are shown in Figs. 3 and 6, oriented that at the smallest β values the condition given by Eq. (4) is such that the Sun is exactly in the −y direction. The image is not satisfied. In such a case, a numerical integral of the Neck- not polluted by any significant ion tail (which should lie close Line brightness should be adopted instead of Eq. (5), which to the +y direction) and is dominated by the Neck-Line dis- always provides F distributions characterized by lower γ val- cussed in the previous sections, which in this period appeared ues, implying higher α values. Therefore, we can conclude that as a perspective dust antitail. In this section we use the inverse the dust population of 67P ejected at 105 days before perihe- tail model to link the dust in the Neck-Line to the dust in the lion is dominated both in mass and in brightness by the largest surrounding tail and the coma close to the nucleus. In fact, the (mm-sized) ejected grains. We can extrapolate this conclusion inverse dust tail model reconstructs a synthetic tail built up by for all the dust ejected from 3.6 AU to 1.7 AU before perihe- dust ejected during a finite time interval. If we choose this time lion, because the Neck-Line has maintained the same shape and interval large enough to cover both the ejection of Neck-Line peak brightness since October 2002 (Fig. 2). dust (about one year before the observations) and the coma dust (a few days before the observations), we can link together the 6. Dust tail fit by means of the inverse model dust parameters during the whole of the 67P activity. The tail model provides dust parameters to be compared with the same The tail images with the best S/N ratio were obtained when quantities obtained by means of the independent Neck-Line comet 67P was observed as target of opportunity by means 364 M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko

Fig. 7. Dust parameters describing the dust environment of 67P during the 2002 perihelion passage. The curves are related to the combinations of the parameters w and u described in Fig. 6. Continuous lines: w = 180◦ and u = −1/2. Dotted lines: w = 90◦ and u = −1/2. Dashed lines: ◦ w = 45 and u = −1/2. Upper-left panel: dust ejection velocity from the inner coma for a reference radius s0 = 5 mm. Lower-left panel: interval of the dust diameters to which all the shown outputs are related. Upper-right panel: power index of the differential size distribution. −1 Lower-right panel: dust mass loss rate (upper curves, kg s )andAfρc values (lower curves, m) of the dust grains inside the size interval shown at left. All curves show an asymmetry between pre and post-perihelion times. See Table 1 for the relationship among t − T,UTandr. photometry, thus testing the reliability of the outputs of both during all the covered times (including the Neck-Line ejection). models. The input TNG images were not calibrated by means The Afρc values allow us also to calibrate absolutely in mag- of standard stars, so that the isophote levels shown in Fig. 6 re- nitudes the isophotes shown in Figs. 3 and 6: we obtain that the fer to arbitrary brightness levels. However, the dust tail model faintest isophote in Figs. 3 and 6 is 26.6 ± 0.3 mag arcsec−2 in also provides the expected Afρc values (A’Hearn et al. 1984): the Cousins R passband, thus confirming that we were unable to detect the IRAS trail by means of the deepest performed s2 s2g(s) Afρ = 2πA (Φ)Q ds (6) CCD observations. c p d v(s) s1 The inverse tail model consists in a least squares fit of the to be compared with the observed Afρo values obtained by surface intensity of the dust tail sampled in 1600 pixels. The means of coma absolute photometry. In Eq. (6), Ap(Φ)isthe output of such a fit is a set of dust parameters that allows us to dust albedo times the phase function, s1 and s2 are the small- minimize the error between the model image and the input im- est and largest dust radii considered by the model, Qd is the age (Fulle 1989). The fits of the observed tail shown in Fig. 6 cumulative dust number loss rate between s1 and s2, g(s)is depend on two parameters describing the dust ejection from the the dust size distribution and v(s) the dust velocity. Therefore, inner coma, u (defined in the previous section) and w,which the comparison between Afρo and Afρc allows us to cali- describes the anisotropy of dust ejection from the inner coma. brate in absolute units (meters) the computed Afρc values Usually, all the u and w combinations provide fits with very provided by the inverse tail model. Since the relationship be- similar errors, so that inverse tail models are unable to disen- tween Afρc and the mass loss rate computed by the inverse tangle the best u and w combination. Here also, as usual, the tail model depends on the dust albedo only, by making the errors of the fits shown in Fig. 6 are very similar (19%, 19% usual assumption that Ap(Φ) = 0.04 we can calibrate in abso- and 20% of the total brightness). But the 67P Neck-Line offers lute units (kg s−1) the dust loss rate provided by the tail model the rare opportunity to select a preferred u and w combination. M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko 365

The parameter u = −1/2 has been determined in the previous To compare the results provided by Neck-Line photom- section by means of Neck-Line photometry, so that the dust etry and inverse tail model, we must take into account that velocity v(s) can be described by the results shown in Fig. 7 were converted from β values to dust diameters by adopting Eq. (1) with a dust bulk density v(s) = v0 s0/s (7) 3 −3 ρd = 10 kg m . In Fig. 7 we can adopt any other value of the becoming equal to v0 at the dust radius s0. The fits of the dust bulk density: this will affect the dust diameter values only. −3 Neck-Line shown in Fig. 6 constrain the best w value. Let us For instance, if ρd = 100 kg m , all the dust diameters should consider the axis of the Neck-Line at the second isophote level: be multiplied by a factor ten, whereas the velocities, loss rates, 4 5 its coordinates are x = −9 × 10 km and y = −2.5 × 10 km. If Afρc and α values will remain the same. At s = 5mmand we join this point to the comet nucleus by means of a straight t − T = −105 days, Fig. 7 provides v = 6.5ms−1 for the most line, we define the observed Neck-Line axis, which crosses the probable u = −1/2andw = 180◦. Such a dust radius corre- 4 5 −4 3 −3 point at x = −6 × 10 km and y = −1.9 × 10 km precisely, sponds to β = 1.2 × 10 for ρd = 10 kg m .Atthisβ,weget i.e. the Neck-Line axis at the second isophote level computed from Fig. 4 a dust velocity close to 4 m s−1: the difference is by means of w = 180◦. The corresponding points related to similar to the uncertainty affecting the obtained dust velocities. w = 90◦ (x = −7 × 104 km and y = −2.0 × 105 km) and For −150 < t − T < −50 days, the size range in Fig. 7 is wider w = 45◦ (x = −8 × 104 km and y = −2.1 × 105 km) do than the β range in Fig. 5, because larger dust sizes are taken 3 −3 not lie on the same observed Neck-Line axis: the stronger the into account, when we consider Eq. (1) with ρd = 10 kg m . anisotropy of dust ejection, the larger the difference in direction The fact that in Fig. 5 we get −3.0 <α<−3.5 while in Fig. 7 between the observed and computed Neck-Lines. Regarding we get −3.5 <α<−3.8 can be due either to a decrease of α the physical meaning of this result, we remember that physical at increasing sizes, or to uncertainties of the inverse tail model models of dust ejection (Crifo & Rodionov 1999; Crifo et al. outputs. In the following, for −150 < t − T < −50 days we will 2004) provide dust flux ratios between the day and night side consider a mean value α = −3.4. of the coma (not the nucleus) smaller than a factor 4. In the schematic approximation adopted here, such a difference be- 7. Comparison with dust coma photometry tween day and night coma sides provides ejection much closer to the w = 180◦ case rather than w = 90◦. In this section we discuss the influence of the finite size inter- Figure 7 shows the dust parameters provided by the in- val inherent in the dust tail model (lower-left panel in Fig. 7) verse tail model. We show the outputs corresponding to all u on the Afρc and mass loss rates curves (lower-right panel in and w combinations considered in Fig. 6, although the Neck- Fig. 7). This discussion for Afρc is very important, because Line fits suggest that only the continuous lines (u = −1/2and all the curves in the lower-right panel of Fig. 7 were cali- w = 180◦) should be taken into account. Fulle (2000) describes brated by means of this quantity and because Afρ depends on the complex procedure to obtain the time-dependent size in- all the quantities shown in Fig. 7. To evaluate how the finite terval (shown in the left-lower panel) inside which all the out- size range influences Afρc, we did the following computations. puts are computed. The Afρc values are certainly lower lim- We selected the most probable u and w parameter combination ◦ its of the observed Afρo, which depend on all ejected dust (u = −1/2andw = 180 ). From the outputs in Fig. 7, we sizes. Therefore, in order to recover the absolute units of Afρc selected sample velocities and size distribution power indices, and mass loss rate, we set the highest Afρc value at t − T = listed in Table 3. Then we assumed that the dust size distribu- 200 days, slightly lower than the Afρo = 0.4 m observed by tion follows a power law with the same index α even outside Lamy et al. (2003) at t − T = 206 days: the next section is de- the size interval covered by the model. Then we computed the voted to a detailed analysis of the comparison between Afρc number loss rates outside this range (Table 3) and the Afρc and Afρo values. Having recovered the absolute values (me- obtained from these new loss rates. In this way we obtained ters) of Afρc, it is possible to obtain the absolute mass loss rate how sensitive the Afρc quantity is to these changes, and how by adopting Ap(Φ) = 0.04. If the albedo is assumed to be 2%, much we can extrapolate the obtained dust parameters outside the mass loss rates become twice as large. the size interval considered by the tail model. Then, if g(s)isa All the other output shows the same unusual asymmetry power law with index α, Eqs. (6), (7), and Fig. 7 yield with respect to perihelion: larger values before than after. The √ + + = −1 s v s1 α − s1 α (α + 3.5) velocity at radius s0 5 mm drops from about 7 m s before = o o 2 1 −1 Qd Afρc (8) perihelion to 2 m s after. The power index α of the differential 3.5+α 3.5+α 2π Ap s − s (α + 1) dust size distribution at the nucleus drops from α = −3.5before 2 1 perihelion to α = −4.5 after. This implies that the dust mass and then Eq. (6) with other values for s1 provides Afρc outside loss rate drops from about 200 kg s−1 before perihelion to about the size range shown in Fig. 7. The results are shown in Table 3, 10 kg s−1 after. The time-independent size distributions, loss and show that the adopted extrapolations of the dust size range rates and dust velocities obtained at −150 < t − T < −50 days imply large changes of Afρc around perihelion only: in partic- are consistent with the spike appearance of the Neck-Line, ular, the rough minimum around perihelion in Fig. 7 becomes which in naive interpretations could suggest an outburst at a well defined maximum at about 50 days after perihelion. The t − T = −105.8 days: the tail brightness peak in the Neck-Line Afρc values in Table 3 were computed adopting a dust radius is uniquely due to the peak of sky-projected dust densities of of 1 cm as upper limit. Since certainly around perihelion much the shells collapsed on the comet orbital plane. larger grains were ejected from the 67P coma, the Afρc values 366 M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko

Table 3. Dust parameters of 67P at several time intervals related to perihelion. α: power index of the diﬀerential dust size distribution (obtained from Fig. 7). v0: dust ejection velocity from the inner coma at the reference dust radius s0 = 5 mm (obtained from Fig. 7). r: Sun-Comet distance. Afρc: computed value over the extrapolated dust radius range between 1 cm and 0.5 µm. Nlay: number of layers per day of grains −1 larger than two microns deposited on a lander at the nucleus surface. Qd [s ]: cumulative dust number loss rate for all the grains with radius larger than s.NoQd value is given when the extrapolation of the size distribution is not supported by any observation.

t − T [days] <−100 −50 0 +50 +150 α −3.4 −3.4 −3.7 −4.0 −4.5 −1 vo [m s ]6.56.05.54.03.0 r [AU] >1.71.41.31.42.1 Afρc [m] 0.10.21.01.70.5 Nlay 0.20.31.11.71.6 03 03 03 02 00 Qd at s > 1cm 1.6 × 10 3.2 × 10 1.4 × 10 2.1 × 10 3.8 × 10 03 04 03 03 01 Qd at s > 5mm 8.5 × 10 1.7 × 10 8.9 × 10 1.7 × 10 4.3 × 10 05 05 05 05 04 Qd at s > 1mm 4.0 × 10 8.1 × 10 6.9 × 10 2.1 × 10 1.2 × 10 05 06 06 05 04 Qd at s > 750 µm8.0 × 10 1.6 × 10 1.5 × 10 5.2 × 10 3.2 × 10 06 06 06 06 05 Qd at s > 500 µm2.2 × 10 4.3 × 10 4.5 × 10 1.7 × 10 1.3 × 10 07 07 07 07 06 Qd at s > 250 µm1.1 × 10 2.3 × 10 2.9 × 10 1.3 × 10 1.5 × 10 08 08 08 08 07 Qd at s > 100 µm1.0 × 10 2.0 × 10 3.5 × 10 2.1 × 10 3.7 × 10 08 09 09 09 08 Qd at s > 50 µm5.5 × 10 1.1 × 10 2.2 × 10 1.7 × 10 4.2 × 10 09 09 09 09 09 Qd at s > 30 µm1.8 × 10 3.7 × 10 8.9 × 10 7.7 × 10 2.5 × 10 09 10 10 10 10 Qd at s > 15 µm9.5 × 10 1.9 × 10 5.8 × 10 6.2 × 10 2.8 × 10 10 10 11 11 11 Qd at s > 10 µm2.5 × 10 5.1 × 10 1.7 × 10 2.1 × 10 1.2 × 10 11 11 12 12 12 Qd at s > 4 µm2.3 × 10 4.6 × 10 2.1 × 10 3.2 × 10 2.9 × 10 12 12 13 13 13 Qd at s > 2 µm1.2 × 10 2.4 × 10 1.3 × 10 2.6 × 10 3.2 × 10 12 13 13 14 Qd at s > 1 µm6.5 × 10 1.3 × 10 8.7 × 10 2.1 × 10 – 13 13 14 15 Qd at s > 0.435 µm4.8 × 10 9.5 × 10 8.2 × 10 2.5 × 10 – 14 14 15 16 Qd at s > 0.203 µm2.9 × 10 5.9 × 10 6.4 × 10 2.5 × 10 – 15 15 16 17 Qd at s > 0.0942 µm1.9 × 10 3.7 × 10 5.1 × 10 2.5 × 10 – 16 16 17 Qd at s > 0.0437 µm1.2 × 10 2.4 × 10 4.1 × 10 –– 16 17 18 Qd at s > 0.0203 µm7.7 × 10 1.5 × 10 3.2 × 10 ––

in Table 3 must still be lower limits to the observed Afρo values. To compute a realistic upper limit to the maximum grain size that can be lifted from the nucleus of 67P, it is necessary to know the 3D shape of the 67P nucleus. Weiler et al. (2004b) obtain ejectable sizes up to 10 cm, but their performed 1D computations are affected by large uncertainties. Therefore, we prefer to stop the integration of Eq. (6) at s2 = 1 cm at all Sun- Comet distances. This assumption affects the extrapolated dust 4 3 mass loss rates, computed by integrating 3 πρd s dQd over all possible dust sizes. Before perihelion only, such a computation provides loss rates lower than those shown in Fig. 7, because in Table 3 we lose the most massive grains: anyway, the loss rate decrease after perihelion is confirmed. The Afρ values in Table 3 must be compared to Afρ val- Fig. 8. Afρo values obtained by means of CCD R-band photometry c o http://cara.uai.it ues to check the reliability of the outputs of the tail models, provided by the CARA network ( ). Diamonds: 1996 perihelion passage. Squares: 2002 perihelion passage. The val- which must provide Afρ values consistent with dust coma c ues show a clear asymmetry with respect to perihelion, with higher photometry after we extrapolate the sizes to all possible val- values after perihelion. This temporal evolution is consistent with the ues. In Fig. 8 we show the available Afρ data covering a o extrapolated Afρc values computed in Table 3, supporting the outputs whole year around two perihelion passages of 67P, provided of the inverse tail model, and is in the opposite sense of the dust mass by CCD photometry of UAI amateur observations. The con- loss rate evolution, due to the large changes with time of the dust size sistence between Afρc values in Table 3 and the Afρo values distribution. in Fig. 8 shows that the dust parameters listed in Table 3 of- fer a schematic summary consistent with all available 67P observations. In particular, the fact that around perihelion grains much larger than 1 cm were probably ejected may account with Afρo = 0.4 m observed by Lamy et al. (2003) at t − T = for the still underestimated Afρc values in Table 3. Moreover, 206 days after perihelion, while Afρc = 0.1 m at 2 AU before Afρc = 0.5matt − T = 150 days in Table 3 is consistent perihelion is consistent with Afρo = 0.16 m observed at 3 AU M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko 367 after perihelion (Schulz 2003). Only a time-dependent index of the nucleus of 67P have been defined. The spin state we α can make consistent the outputs of the tail model (Fig. 7) have suggested here will be used as input of 3D thermal mod- with the Afρo values (Fig. 8): a time-independent dust size els of the 67P nucleus, assuming that the torques due to the distribution with α = −3.5 at mm sizes and α = −4.5at gases leaving the surface change this state on timescales much micron sizes would be consistent with the results shown in longer than the comet orbital period. If this is the case, nucleus Fig. 7, but would provide Afρc values much higher than Afρo photometry performed during the aphelion might constrain the at t − T > 100 days. spin state proposed here. We cannot exclude other explana- tions, based on a homogeneous nucleus where dust fragmentation is active after perihelion only. Also realistic models able 8. Future models of the 67P nucleus to describe this second possibility require detailed information The temporal evolution of all the quantities shown in Fig. 7 of the nucleus shape, topography and spin state, i.e. the same suggests seasons of a comet nucleus characterized by an in- information required by the seasonal scenario we are proposing homogeneous surface, following a similar interpretation of the here. No realistic dust fragmentation model in a realistic coma outputs of the same tail model applied to Comet 2P/Encke is now available (Crifo & Rodionov 1999). (Epifani et al. 2001). Let us assume that both the obliquity of If 3D thermal models of the 67P nucleus confirm that the the spin axis of the nucleus and its angle with the perihelion- proposed seasons can explain the time evolution of the gas loss aphelion line are closer to 90◦ than to zero: then, one hemi- rates, we still have to explain how these seasons affect the mass sphere of the nucleus (let us call it the northern one) will be dust loss rate during the whole 67P orbit. The proposed sea- the only one to be exposed to Solar radiation before perihelion, sonal scenario predicts that the mass loss rate remains at the while after perihelion only the southern one will be heated by low post-perihelion values (about 10 kg s−1) during all the post- the Sun. During the 1982 perihelion passage, the gas produc- perihelion times, possibly decreasing towards the aphelion. The tion rates (A’Hearn et al. 1995; Cochran et al. 1992) for OH, Neck-Line data suggest that at 3.6 AU pre-perihelion the mass −1 CN, C3,C2 and NH were systematically higher after perihe- loss rate increases from 10 kg s (or much less according to lion than before. Within our hypothesis, this gas loss asymme- which dust size CO and water can lift up) to the 100 kg s−1 try suggests that the ice fraction of the northern hemisphere is typical of the pre-perihelion times in Fig. 7. This is due to the larger than that of the southern one. The output shown in Fig. 7 size distribution of the grains covering (in our speculative sce- requires that the dust covering the two hemispheres is char- nario) the northern hemisphere, which is dominated by mm acterized by different physical parameters. For instance, if the and cm-sized grains. Neck-Line data require that the gas at northern hemisphere is characterized by a dust size distribution 3.6 AU pre-perihelion is dense enough to lift these large grains. 3 −3 with many more mm and cm-sized grains than the southern If the nucleus is a sphere with ρn = 10 kg m and ejects at one, we directly explain the temporal evolution of the index α least 5 × 1027 s−1 CO molecules, then cm-sized spheres with 3 −3 in Fig. 7. This scenario implies that the temporal evolution of ρd = 10 kg m are ejected all around the comet orbit, but will the dust mass loss rate becomes opposite to the temporal evolu- dominate both dust mass and coma brightness before perihe- tion of the gas loss rates and of the dust coma brightness: while lion only, due to the temporal evolution of the dust size distri- the dust mass loss rate reaches the largest values before perihe- bution. IRAM observations (Bockelee-Morvan et al. 2004) per- 27 −1 lion, the dust coma brightness and the gas loss rates reach the formed at 3 AU after 2002 perihelion gave QCO < 1.6×10 s , largest values after perihelion. but this result cannot be extrapolated to the corresponding dis- The temporal evolution of the dust ejection velocity in tances before perihelion: other observations are required when Fig. 7 seems to require a relationship between the dust size the comet will reach 3.6 AU before perihelion. If the total gas and the β parameter which is more complex than Eq. (1). The loss rate (water and CO) at 3.6 AU before perihelion will turn β parameter describes the ratio between solar radiation pressure out to be much lower than the required 5×1027 mol s−1, then the and gravity forces on a dust grain, so that it depends on the ra- Neck-Line data suggest that both ρd and ρn may be much lower tio between the grain cross section and mass. However, the gas than 103 kg m−3,and/or that the nucleus and/or the dust grains drag efficiency on a grain also depends on the ratio between its are non-spherical. Crifo et al. (2004) have recently computed a cross section and mass. The dust velocities in Fig. 7 are lower 3D model of a gas coma surrounding a non-spherical 67P nu- 2 −3 27 −1 post- than pre-perihelion, despite higher gas coma densities af- cleus (with ρd = ρn = 10 kg m ) ejecting 10 CO mol s ter perihelion than before. This apparent contradiction suggests and 2.5 × 1026 water mol s−1 at 3 AU: this coma ejected dust that realistic models of the drag due to gas and that due to solar spheres of 5 cm radius. radiation pressure should also take into account the spin state The IRAS trail data collected by Sykes & Walker (1992) of non-spherical grains. β might depend on the grain shape and can be compared with the dust environment obtained in this spin state, which may be different in the coma and in the tail. paper. They assume that the dust sizes dominating the trail This fact does not affect the outputs of the tail models adopted brightness are characterized by β = 10−3. After we correct this in this paper, which are all related to β values: it simply sug- β value to the more proper value β = 10−4 (see Fig. 5), we gests that the conversion from β to dust sizes is more complex find that the total dust mass in the trail is 3 × 109 kg. Sykes & than Eq. (1). Walker (1992) conclude that the very short 67P trail must have The proposed seasonal scenario will remain speculative un- been ejected during the previous perihelion passage only: ac- til 3D models of the thermal evolution of the 67P nucleus will cording to the seasonal scenario we are proposing here, we can be available: these are impossible until the shape and spin state assume that all the trail mass was ejected from 3.6 to 1.3 AU 368 M. Fulle et al.: The dust environment of comet 67P/Churyumov-Gerasimenko before perihelion, i.e. during one year only before perihelion consistent with such a scenario; (vi) the first dust monolayer (see Table 1). Then, the total IRAS 67P trail mass yields ex- will be collected by the lander in the first week; (vii) the first actly the dust loss rate of 100 kg s−1 obtained in this paper. dust monolayer will be collected by the orbiter in the first four months spent at distances less than 10 km from the nucleus; (viii) since the dust brightness is dominated by, or at least 9. Conclusions significantly depends upon the largest ejected grains, spurious During its approach to its target comet, the Rosetta probe will identifications of stars by the navigation cameras is a primary face a dust environment dominated both in mass and in bright- danger for the mission: robust software against false nucleus ness by cm-sized grains released at a rate of 100 kg s−1.The detection is mandatory. previous Rosetta target, 46P/Wirtanen, was characterized by a dust mass loss rate 100 times lower at 2.5 AU before perihelion, but very similar at perihelion (Fulle 2000): the seasonal References scenario proposed in the previous section might explain this A’Hearn, M. F., Schleicher, D. G., Feldman, P. D., Millis, R. L., & ff strong di erence in terms of a dust-to-gas ratio in 67P much Thompson, D. T. 1984, AJ, 89, 579 higher than in 46P. This explanation is consistent with the simi- A’Hearn, M. F., Millis, R. L., Schleicher, D. G., Osip, D. J., & Birth, lar water loss rate and the different nucleus sizes of 67P and 46P P. V. 1995, Icarus, 118, 223 (4 km vs. 1.5 km, Lamy 2003). However, all these facts do Bockelee-Morvan, D., Moreno, R., Biver, N., et al. 2004, Proc. of The not help us to define what is a representative comet (Weissman New Rosetta Targets Meeting, in press 1999). Brandt, J. C., Roosen, R. G., & Harrington, R. S. 1972, ApJ, 177, 277 The extrapolations given in Table 3 allow us to compute Burns, J. A., Lamy, P. L., & Soter, S. 1979, Icarus, 40, 1 Cochran, A. L., Barker, E. S., Ramseyer, T. F., & Storrs, A. D. 1992, the number Nlay of layers per day of dust grains larger than two microns (for smaller grains the extrapolations may become Icarus, 98, 151 Cremonese, G., & Fulle, M. 1989, Icarus, 80, 267 arbitrary) deposited on a lander at the nucleus surface: Crifo, J. F., & Rodionov, A. V. 1999, Plan. Space Sci., 47, 797 2 Crifo, J. F., Lukyanov, G. A., Zakharov, V. V., & Rodionov, A. V. 2004, s (α + 1) Qd ∆t N = 1 (9) Proc. of The New Rosetta Targets Meeting, in press lay + 2 4(α 3) Rn Epifani, E., Colangeli, L., Fulle, M., et al. 2001, Icarus, 149, 339 ESA 2003, Proc. of the 12th RSWT, 13 Feb. 2003 where s1 = 2 µm, Qd and α are reported in Table 3, ∆t = 8.64 × 104 sandR = 2 km is the nucleus radius (Lamy et al. Fulle, M. 1988, A&A, 201, 161 n Fulle, M. 1989, A&A, 217, 283 2003). The number of layers may be overestimated because we ffi Fulle, M. 1999, Plan. Space Sci., 47, 827 consider a sticking coe cient equal to one, while it is probable Fulle, M. 2000, Icarus, 145, 239 that not all grains will stick on the probe surfaces. Moreover, Fulle, M., & Sedmak, G. 1988, Icarus, 74, 383 the lander itself will shadow some of the surface below it, thus Fulle, M., Bosio, S., Cremonese, G., et al. 1993, A&A, 272, 634 stopping the water (not the CO) gas release. On the other hand, Kimura, H., & Liu, C. P. 1977, Chin. Astron., 1, 235 we are neglecting the high flux of large grains falling on the lan- Lamy, P. L., Toth, I., Weaver, H., Jorda, L., & Kaasalainen, M. 2003, der from above (Crifo et al. 2004). We find that already at the A&AS, DPS 35, 30.04 Rosetta lander delivery planned at 3 AU, a lander may collect Pansecchi, L., Fulle, M., & Sedmak, G. 1987, A&A, 176, 358 a monolayer of grains larger than two microns every five days, Reach, W. T., Hicks, M. D., Gillam, S., et al. 2003, A&AS, DPS 35, while the Rosetta probe orbiting at a distance of 10 km from 30.07 the nucleus will collect the first monolayer of grains larger than Schulz, R. 2003, Abstract Book of The New Rosetta Targets Meeting, 10 two microns after the first four months. Sekanina, Z., & Schuster, H. E. 1978, A&A, 65, 29 Table 3 is a comprehensive summary of the dust environ- Sykes, M. V., & Walker, R. G. 1992, Icarus, 95, 180 ment of 67P consistent with all available observations. The dust UAI 2003, Comet Archive, environment from 3.6 AU to perihelion, i.e. during all the time http://comete.uai.it/67p/index.htm the Rosetta probe will spend orbiting around the comet, can be Weiler, M., Rauer, H., & Helbert, J. 2004a, A&A, 414, 749 summarized by the following eight points: (i) grains larger than Weiler, M., Knollenberg, J., & Rauer, H. 2004b, Proc. of The New 1 cm are ejected from the coma; (ii) the mass loss rate is larger Rosetta Targets Meeting, in press than 100 kg s−1; (iii) the mass loss rate is dominated by the Weissman, P. 1999, in Composition and Origin of Cometary Materials, largest ejected grains; (iv) the dust coma brightness (e.g. ed. K. Altwegg et al. (Kluwer), 301 the Afρ quantity) depends significantly or even mainly Yeomans, D. K., & Wimberly, R. N. 1991, in Comets in the Post- upon the largest ejected dust grains; (v) a low Afρ = 0.1mis Halley Era, ed. R. L. Jr. Newburn et al., 2, 1281